This invention relates generally to optical devices, and more particularly to photonic band gap structures and sub-wavelength grating structures.
Light has several advantages over the electron. As used herein, xe2x80x9clightxe2x80x9d means not only signals in the spectrum of visible light, but also signals in the full spectrum of frequencies typically handled by optical transmission systems. The speed of light is approximately three orders of magnitude higher, compared to the speed of electrons in semiconductors. Thus, photons of light can theoretically carry information approximately 1,000 times faster than electrons in semiconductors. Moreover, photons are not as strongly interacting as electrons with their environment, which allows photonic devices to dissipate less energy, produce less heat and generate less signal noise compared to electronic devices.
In spite of the numerous advantages of photons, all optical circuits have yet to be commercially available on a large scale. Some hybrid opto-electronic circuits have produced significant improvement over the performance of electronic circuits, but the difficulties in designing a multipurpose optical component analogous to the electronic transistor has severely hindered the development of all optical systems.
It is known that as the periodicity of a medium becomes comparable with the wavelength of electromagnetic waves traveling therethrough, the medium begins to significantly inhibit the wave""s propagation. A photonic band gap (PBG) structure is one type of optical structure that is currently being investigated for certain electromagnetic (EM) wave applications. PBG are formed from photonic crystals, which are composite periodic structures made up of two different dielectric materials. Both of the dielectric materials should be nearly transparent to electromagnetic radiation in the frequency range of interest. However, the composite periodic structure may not be transparent to the frequency range of interest, due to electromagnetic scattering at the interfaces between the two dielectric components. Intervals of prohibited frequencies are called photonic band gaps.
Relying on the subwavelength wave inhibition effect, PBG structures are two or three-dimensional periodic array structures in which the propagation of EM waves may be described by band structure types of dispersion relationships resulting from scattering at the interfaces between the two dielectric components. Waveguide dispersion is the term used to describe the process by which an electromagnetic signal is distorted by virtue of the dependence of its phase and group velocities on the geometric properties of the waveguide. These photonic band gap structures provide electromagnetic analogs to electron-wave behavior in crystals, with electron-wave concepts such as reciprocal space, Brillouin zones, dispersion relations, Bloch wave functions, Van Hove singularities and tunneling having electromagnetic counterparts in a PBG. This has enabled the development of many new and improved types of photonic band gap devices, including devices in which optical modes, spontaneous emission, and zero-point fluctuations are substantially reduced.
PBG structures can also be formed with added local interruptions in an otherwise periodic photonic crystal, thereby generating defect or cavity modes with discrete allowed frequencies within an otherwise forbidden photonic band gap range of frequencies. Generation of an allowed defect state in an otherwise forbidden band gap enables applications such as high-Q resonators or filters.
In the absence of external currents and sources, Maxwell""s equations for a photon in a dielectric waveguide may be represented in the following form:             {              ∇                  xc3x97                      1                          ϵ              ⁡                              (                r                )                                              ⁢                      ∇            xc3x97                              }        ⁢          H      ⁢              (        r        )              =                    ω        2                    c        2              ⁢          H      ⁢              (        r        )            
where H(r) is the magnetic field of the photon, xcfx89 is its frequency, c is the speed of light and ∈(r) is the macroscopic dielectric function of the waveguide. The solutions H(r) for and xcfx89 are determined completely by the magnitude and symmetry properties of ∈(r). If ∈(r) is perfectly periodic, as in a photonic crystal comprising a dielectric waveguide having a periodic array of embedded features, such as a series of holes etched into the waveguide, the solutions to Maxwell""s equation are quantized, characterized by a wavevector k and a band index n. Thus, the periodicity of the waveguide dielectric constant removes degeneracies that would otherwise allow free photon states at the Bragg plane, forming a photonic band gap. The region of all allowed wavevectors is referred to as a Brillouin zone and the collection of all solutions to the above equation is termed a band structure. Thus, in a perfectly periodic photonic crystal, allowed photonic states are quantized, with band gaps having no allowed states between discrete allowed states.
When a periodic array of features, such as holes, is introduced into a waveguide material to form a perfectly periodic photonic crystal, the wavevector k becomes quantized and limited to xcfx80/a, where a is the spatial period of the holes. In addition to putting a limit on wavevector values, the introduction of an array of holes in a waveguide has the effect of folding the dispersion relations (xcfx89n(k)) of the strip waveguide and splitting the lowest-order mode to form two allowable guided modes. The splitting at the Brillouin zone edge is referred to as a band gap. The size of the band gap is determined by the relative dielectric constants of the waveguide material and the material filling the periodic structures, such as air in the case of holes. The larger the difference in relative dielectric constants, the wider the gap.
If a defect is included into an otherwise periodic PBG structure, an allowed photonic state can be created within the band gap. This state is analogous to a defect or impurity state in a semiconductor which introduces an energy level within the semiconductor""s band gap. A defect in the otherwise periodic PBG structure is formed by incorporating a break in the periodicity of the PBG structure. PBG defects can take the form of a spacing variation using constant features, use features having a different size or shape, or use a different material. Introduction of a PBG defect may result in the creation of a resonant wavelength within the band gap.
The resonant wavelength of a PBG structure may be shifted by changing the defect. For example, a PBG structure using a defect in feature spacing can shift the resonant wavelength by altering the length of the defect in feature spacing. Increasing the defect spacing length increases the resonance wavelength to a longer value and also reduces the cavity""s Q. The Q of an optical resonant cavity is its figure of merit, defined as 2xcfx80xc3x97 (average energy stored in the resonator)/(energy dissipated per cycle). The higher the reflectivity of the surfaces of an optical resonator, the higher the Q of the resonator and the less energy loss from the desired mode. An increase in defect length results in a corresponding increase in the effective refractive index felt by the resonant mode due to a reduced density of lower refractive index holes in the higher refractive index waveguide material. The increase in the effective refractive index of the waveguide material results in the reduction of the frequency of the resonant mode. This reduction enhances the coupling of the resonant mode to the waveguide mode. This increases the cycle average radiation out of the cavity resulting in a lower Q. A reduction in defect spacing length is expected to produce the inverse result.
Alternatively, the feature spacing, such as hole spacing, may be held constant, but a column of holes having a different size compared to the other PBG holes may be used to introduce an allowed photon state within the PBG band gap. For example, a column of holes may be placed in the PBG hole array having a radius greater or less than the nominal hole radius. As a further alternative, a row of PBG holes filled with a material having a refractive index higher or lower than the material filling the other PBG holes may be used to create an allowed photon state within the PBG band gap. Any of the above techniques may be combined.
Referring to FIG. 1(a), an example PBG structure 100 having a spacing defect is shown. Eight substantially cylindrical holes 101-108 are embedded in silicon waveguide 109. Waveguide 109 has a width 113 of 0.47xcexc and thickness 114 of 0.2xcexc, which can be supported by silicon dioxide cladding layer 110. Holes 101-108 shown are cylindrical having a radius (r) of 0.1xcexc. The center to center spacing 111 (denoted as xe2x80x9caxe2x80x9d) between holes 101 and 102 is 0.42xcexc and equivalent to the distance between holes 102 and 103, 103 and 104, 105 and 106, 106 and 107 and 107 and 108. However, the spacing between holes 104 and 105, 112 (denoted as ad), is not equal to 0.42xcexc. Rather, this distance 112 is 0.63xcexc, 50% more than the nominal hole spacing (a).
FIG. 1(b) illustrates the spectral response of the PBG structure 100 etched in a silicon waveguide, as shown in FIG. 1(a). The large contrast of dielectric constants between the silicon waveguide (∈Si=12.1) and PBG features filled with air (∈air,=1) creates a correspondingly wide band gap from between approximately 1300 nm to 1700 nm, or nearly 400 nm as shown in FIG. 1(b). A band gap functions as a stop band. The narrow resonance transmission peak centered at approximately 1540 nm results from placing a spacing defect into the PBG hole array which is otherwise comprised of equally spaced holes. The PBG structure shown in FIG. 1(a) has a calculated cavity quality factor Q of approximately 280 at the resonant wavelength.
Sub-wavelength structures (SWS) are a second type of optical structure. Grating structures are generally known in the art to provide a method of dispersing incident electromagnetic wave energy. In particular, gratings comprising periodic elements have been used to diffract light incident on a grating created by periodic slits cut into a given material. When light is incident on the surface of a single diffraction grating, the light may be reflected (or backward diffracted) and/or transmitted (or forward diffracted) at angles that depend upon the periodicity of the grating relative to the wavelength of the incident light and the light""s angle of incidence. By the process of diffraction, light can be separated into its component wavelengths thereby forming a spectrum that can be observed, photographed, or scanned photoelectrically or thermoelectrically. Diffraction gratings can be used to influence the amplitude, phase, direction, polarization, spectral composition, and energy distribution of a beam of light. Gratings are therefore used in common instruments such as spectroscopes, spectrometers, and spectrographs.
Optical wavelength may be defined as the wavelength of an EM wave in a given material and is equal to the wavelength of the wave in a vacuum divided by the material""s refractive index. As the period of the grating approaches the optical wavelength of the incident radiation, the diffracted orders begin propagating at increasingly larger angles relative the surface normal of the grating. Eventually, as the grating period is reduced and approaches the optical wavelength of the incident radiation, the angle of diffraction approaches 90 degrees, resulting in propagation of the radiation confined to the plane of the grating. This subwavelength condition effectively couples the fields of the incident radiation within the grating structure, a direction transverse to the surface normal of the grating.
An example of the formation and use of a subwavelength grating structure is described in U.S. Pat. No. 6,035,089, by Grann, et. al (xe2x80x9cGrannxe2x80x9d), which is assigned to Lockheed Energy Research Corporation, predecessor to the assignee of the current application. The entire contents of U.S. Pat. No. 6,035,089 are hereby incorporated by reference. Grann describes a single subwavelength grating structure (SWS) that uses periodically spaced high refractive index xe2x80x9cpostsxe2x80x9d embedded in a lower refractive index dielectric waveguide material to form an extremely narrowband resonant reflector.
A subwavelength grating structure which functions as a zeroth order diffraction grating can be represented by an effectively uniform homogeneous material having an effective refractive index (neff). Under particular incident wave configurations, such as a substantially normal incident beam, and certain structural constraints, such as the refractive index of the medium surrounding the grating less than refractive index of the waveguide less than refractive index of the posts, a subwavelength structure may exhibit a resonance anomaly which results in a strong reflected beam over an extremely narrow bandwidth. If the incident radiation is not within the SWS resonant bandwidth, most of the energy of the incident beam will propagate through the grating in the form of a transmitted beam.
This resonance phenomenon occurs when electromagnetic radiation is trapped within the grating material due to total internal reflection. If this trapped radiation is coupled into the resonant mode of the SWS grating, the field will resonate and redirect substantially all of the electromagnetic energy backwards. This resonance effect results in a nearly total reflection of the incident field from the surface, which may be designed to be extremely sensitive to wavelength.
Grann""s embedded grating structure results in minimal sideband reflections. Since Grann""s resonant structure is buried within a waveguide, both the input and output regions of the grating share the same refractive index, resulting in minimal or no Fresnel reflection losses. Thus, reflection losses are minimized permitting operation as an extremely reflective resonant grating.
Reflective gratings may be combined to perform functions that a single reflective grating is incapable of realizing. For example, a Fabry-Perot interferometer may be constructed by combining two flat highly reflective plates. Fabry-Perot plates are generally set parallel to one another and separated by an optical path length equal to an integral number of half wavelengths of a desired wavelength so that light of a desired wavelength bounces back and forth between the plates multiple times. Optical path length is the physical separation distance between the mirrors multiplied by the refractive index of the waveguide. For a given plate spacing the requirement for constructive interference being an optical path length equal to an integral number of half wavelengths of the incident radiation of a given wavelength can be fulfilled only at particular incident angles, relative to the surface normal of the plates. Therefore, Fabry-Perot interferometers can be used as spectrometers with high resolution as well as optical resonators. Used as a laser resonator, the Fabry-Perot reinforces only light of specific wavelengths traveling perpendicular to the mirror surfaces, and its successive reflections and amplifications form an oscillating mode, creating an optical resonator.
The invention involves a transverse-longitudinal integrated optical resonator (TLIR) which comprises a waveguide, a first and a second subwavelength resonant grating in the waveguide and a photonic band gap resonant structure (PBG) having a plurality of features in the waveguide. The PBG is positioned between the first and second subwavelength resonant gratings. The first and second subwavelength resonant gratings and the PBG features may be embedded in the waveguide. The waveguide may be selected from the group of materials consisting of Si, Ge, ZnSe, BaF2, CdTe, LiNbO3 and SBN. The TLIR may further comprise at least one cladding layer positioned adjacent to the waveguide. Cladding layers have a lower index of refraction than the waveguide and may be selected from the group consisting of glasses and BaF2.
The waveguide may be formed from an electro-optic material and the cladding layers may comprise at least one lower buffer layer positioned under the waveguide and at least one upper buffer layer positioned over the waveguide. The TLIR may further comprise a pair of electrically conductive discharge electrodes, wherein the waveguide is positioned between the electrically conductive discharge electrodes, the electrically conductive discharge electrodes being separated from the waveguide by the buffer layers. The TLIR may further comprising a bulk substrate material and a RF oscillator, wherein the RF oscillator is formed on the bulk substrate material and is electrically connected to the electrically conductive discharge electrodes.
The PBG can comprise at least one row of PBG features having at least one defect therein. Defects may be selected from the group consisting of a spacing defect, a size defect and a refractive index defect. PBG features include holes which may be filled with a gas, such as air. PBG features may be arranged in linear arrays.
Each subwavelength resonant grating structure can comprise a substantially periodic array of SWS features. SWS features from the first and second resonant grating may be arranged in substantially linear arrays or arranged along arcs having a radius of curvature.
PBG features may also be arranged along arcs having a radius of curvature. SWS features can be formed from materials having a refractive index higher than that of the waveguide material. SWS features may be formed materials such as Ge, BaF2, LiNbO3, SBN and Si.
The resonator formed by the first and second resonant gratings may have a first transmission resonance and the PBG may have a second transmission resonance, wherein the transmission resonances are substantially equal. The TLIR may sustain substantially one or more propagating modes.
TLIR may further comprise a bulk substrate material having a plurality of die, the die each having at least one electronic device, wherein the TLIR is positioned on the die. TLIR can be communicably connected to one or more of electronic devices and may further include a structure for cooling.
A composite optical resonator can be formed comprising at least two transverse-longitudinal integrated optical resonators connected in series or in parallel. A gas detector can be formed from a plurality of TLIRs, comprising a plurality of transverse-longitudinal integrated optical resonators (TLIR) connected in parallel, wherein the plurality of TLIRs exhibit transmission resonances centered at more than one wavelength. The gas detector may further include a bulk substrate material having plurality of die, wherein the gas detector can be positioned on the die.
A method for tuning the transmission resonance of a TLIR comprises the steps of providing a first and second subwavelength resonant grating structure in a waveguide, providing a photonic band gap resonant structure (PBG) in the waveguide, wherein the PBG is positioned between the first and second subwavelength resonant grating structures and tuning at least one of the transmission resonances to result in the transmission resonances being substantially equal. Preferably, being subtantially equal is when a ratio of the nominal transmission resonance wavelength (xcex) divided by the spread in resonant wavelengths (xcex94xcex) is less than the square root of the product of the PBG Q and the first and second subwavelength grating structure Q. In this context, the nominal transmission resonance wavelength (xcex) may be defined as the arithmetic mean of the PBG transmission resonant wavelength and the transmission resonant wavelength of the resonator formed by SWS gratings. Most preferably, the ratio of the nominal transmission resonance wavelength (xcex) divided by the spread in transmission resonant wavelengths (xcex94xcex) is less than xc2xd the square root of the product of the Qs of the individual resonators. Tuning can be accomplished through electo-optic, photo-refractive, thermal, magneto-optic or tilting, or a combination of these methods.
The TLIR can process electromagnetic signals. The TLIR can be used for optical computing, optical signal modulation and wavelength division de-multiplexing.
A method of forming a TLIR comprises the steps of providing a first and second subwavelength resonant grating structure in a waveguide, providing a photonic band gap resonant structure (PBG) having a plurality of features in the waveguide, wherein the PBG is positioned between the first and second subwavelength resonant grating structure. The TLIR may be formed in a waveguide positioned on a bulk substrate material, the bulk substrate material having a plurality of die, including the steps of selecting the die, providing a first and second subwavelength resonant grating structure in the waveguide, and providing a photonic band gap resonant structure (PBG) having a plurality of features in the waveguide, wherein the PBG is positioned between the first and second subwavelength resonant grating structure. The method of forming a TLIR may further comprise a step of planarizing the waveguide and may comprise the step of providing at least one cladding layer, the at least one cladding layer formed over the bulk substrate. The cladding layer may comprise at least one lower buffer layer under the waveguide and at least one upper buffer layer over the waveguide.
The method of forming a TLIR may further comprise the steps of forming a first electrically conductive film over the at least one lower buffer layer and forming a second electrically conductive film over the upper buffer layer. The electrically conductive films each form electrically conductive discharge electrodes. The waveguide is positioned between the electrically conductive discharge electrodes, the electrically conductive discharge electrodes being separated from the waveguide by the buffer layers. The method may also include the step of forming an RF oscillator on the bulk substrate material, the RF oscillator electrically connected to the electrically conductive discharge electrodes.
A broadband reflective mirror comprises a waveguide having a first refractive index, and a subwavelength grating having a plurality of SWS features positioned with a substantially equal spacing. The SWS features are formed from at least one material having a second refractive index greater than the first refractive index, wherein incident photons within the broadband reflective mirror""s bandwidth are substantially reflected. The waveguide may be formed from at least one electro-optic material, such as CdTe, LiNbO3 and SBN. The waveguide can be a substantially planar waveguide, and the broadband mirror may further comprise at least one cladding layer positioned adjacent to the planar waveguide.
A method for determining a post grating period to form a broadband reflective mirror having a given center resonant wavelength comprises selecting a waveguide material having a first refractive index, selecting a post material having a second refractive index, the second refractive index greater than the first refractive index, and calculating a post grating period from factors including the center resonant wavelength, the first refractive index and the second refractive index.
A method for forming a broadband reflective mirror comprises the steps of selecting a waveguide having a first refractive index, and providing a subwavelength grating in the waveguide. The subwavelength grating has a plurality of SWS features positioned with a substantially equal spacing, the SWS features formed from at least one material having a second refractive index greater than the first refractive index. The subwavelength grating may be embedded in the waveguide. The broadband mirror can be used to process electromagnetic signals, including applications such as LIDAR and notch filtering.
A narrowband resonant transmitter comprises a waveguide having a first refractive index, and a first and second subwavelength resonant grating structure in the waveguide, the resonant gratings separated by a spacing distance, wherein incident photons over a narrow range of wavelengths are transmitted by the resonant transmitter. The narrow range of wavelengths are approximately determined by the spacing distance between the resonant gratings and the first refractive index. The narrowband resonant transmitter may comprise a waveguide formed from at least one electro-optic material, such as CdTe, LiNbO3 and SBN. The narrowband resonant transmitter may also include a substantially planar waveguide, and further comprise at least one cladding layer positioned adjacent to the planar waveguide.
The narrowband resonant transmitter may further comprise a pair of electrically conductive discharge electrodes, wherein the waveguide is positioned between the electrically conductive discharge electrodes, the electrically conductive discharge electrodes being separated from the waveguide by the buffer layers. The narrowband resonant transmitter may further comprise a bulk substrate material and an RF oscillator, wherein the RF oscillator is formed on the bulk substrate material and is electrically connected to the electrically conductive discharge electrodes.
A method for forming a narrowband resonant transmitter comprises the steps of selecting a waveguide having a first refractive index, and providing a first and second subwavelength resonant grating structure in the waveguide. The resonant gratings are separated by a spacing distance, wherein the transmission resonance is approximately determined by the spacing distance and the first refractive index. The waveguide can be electro-optic. The narrowband transmitter equipped with an electro-optic waveguide can process electromagnetic signals for applications including electro-optic modulation.
The method of forming a narrow band resonant transmitter may further comprise the step of providing at least one cladding layer, the at least one cladding layer formed over a bulk substrate material. The at least one cladding layer may comprise at least one lower buffer layer under the waveguide and at least one upper buffer layer over the waveguide. The method may further comprise the step of forming a first electrically conductive film over the at least one lower buffer layer and forming a second electrically conductive film over the at least one upper buffer layer, the electrically conductive films each forming conductive discharge electrodes. The waveguide can be positioned between the electrically conductive discharge electrodes, the electrically conductive discharge electrodes being separated from the waveguide by the buffer layers. The method of forming a narrow band resonant transmitter may further comprise the step of forming an RF oscillator on the bulk substrate material, the RF oscillator being electrically connected to the electrically conductive discharge electrodes.
The narrowband transmitter may further comprise a bulk substrate material having a plurality of die, each die having at least one electronic device, wherein the narrowband resonant transmitter is positioned on the die. The narrowband resonant transmitter can be communicably connected to the one or more electronic devices on the die. The narrowband transmitter can be used for processing an electromagnetic signal including electro-optic modulation.